202 research outputs found
Solving eigenvalue PDEs of metastable diffusion processes using artificial neural networks
In this paper, we consider the eigenvalue PDE problem of the infinitesimal
generators of metastable diffusion processes. We propose a numerical algorithm
based on training artificial neural networks for solving the leading
eigenvalues and eigenfunctions of such high-dimensional eigenvalue problem. The
algorithm is able to find multiple leading eigenpairs by solving a single
training task. It is useful in understanding the dynamical behaviors of
metastable processes on large timescales. We demonstrate the capability of our
algorithm on a high-dimensional model problem, and on the simple molecular
system alanine dipeptide.Comment: revision with minor change
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